Help very bad due in 10 mins
1 answer:
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<h3>Answer:</h3>
<em>Try the answers</em>
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
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<em>Derive it</em>
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
